\theoremstyle{plain}% default
\newtheorem{theorem}{Theorem}[section]
\newtheorem*{theorem*}{Theorem}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem*{lemma*}{Lemma}

\theoremstyle{definition}
\newtheorem*{definition}{Definition}
\newtheorem{conjecture}{Conjecture}
\newtheorem*{conjecture*}{Conjecture}
\newtheorem{example}{Example}[section]

\theoremstyle{remark}
\newtheorem*{remark}{Remark}
\newtheorem*{note}{Note}

\DeclareMathOperator{\Prob}{Prob}
\DeclareMathOperator{\ord}{ord}
\DeclareMathOperator{\head}{head}
\DeclareMathOperator{\tail}{tail}
\DeclareMathOperator{\Tree}{Tree}
\DeclareMathOperator{\Irred}{Irred}
\DeclareMathOperator{\IrSelTr}{IrSelTr}
\DeclareMathOperator{\SIT}{SIT}
\DeclareMathOperator{\SSIT}{SSIT}
\DeclareMathOperator{\GnB}{\mathcal{G}_{n,B}}
\DeclareMathOperator{\Gnd}{\mathcal{G}_{n,d}}

\newcommand{\Rayleigh}[2]{\mathcal{R}_{#1}(#2)}